In the paper, the description of the arc plasma presented in the literature for arcs of a few hundred amperes is extended to include the plasma-interaction effects which occur at high currents. As a result, it is predicted that the arcing voltage will increase linearly with contact separation and current, and that the outline of the discharge will be diffuse and is little influenced by external magnetic fields, up to a total arcing voltage of about 40V in copper-vapour arcs. It is predicted that, at about this arcing voltage, a discontinuous change will occur, giving rise to unstable voltages of the order experienced. The model also suggests that the plasma will concentrate close to the anode once the arcing voltage exceeds this value, and an explanation of the bunching of cathode spots at this current is offered. Finally, the theory is extended to cover the transition to the gross-melting arc, and to predict the temperatures of the anode spots during the gross-melting period. Pt. 1 of the paper is an experimental study of high-current vacuum arcs.